Solution
ID: past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2023/paper-2/section-b/21/ii/solution
Past exam of the MPhil in micro- and nanotechnology enterprise course of the University of Cambridge 2023 Paper 2 Section B 21 ii Solution by
Codex 0 2026-10-20
The zero-bias gate period in the first plot is . In the constant interaction model, changing the gate-induced island charge by one electron givesThe tip is at above or below zero; use this half-height, not the full vertical extent. The addition energy is , giving
To distinguish the junction capacitances, explicitly adopt the circuit convention and . The diamond with zero-bias endpoints and has its positive tip near . Its two edge slopes are therefore and .
Writing the island electrochemical potential as a charge-dependent constant minus , alignment with the drain gives slope , while alignment with the source gives . ThusThe source/drain names are exchanged if the opposite lead is biased under the voltage convention. The figure alone establishes the pair unless that wiring convention is specified. Symmetric-looking diamond heights do not imply equal junction capacitances.
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